Math 154A Final Exam Review

 

Your final exam is December 8th, 1-2:50 pm, Room A213.  Since the exam is comprehensive, this is a list of some of the more “difficult” concepts that we studied in Fall, 2011.  The final covers all of the sections of the book that we worked in throughout the quarter.  You should bring your calculator, and a straight-edge for graphing.  Approximately one fourth of the exam will be on Chapter 14.

 

1.  Solve   a)  82x-1         = 163x        b)  log4 (3x) = 2                   c)  ln (5x-7) = 3

 

  1. Solve the inequality x2 -3x >  4  Write your solution in interval notation and on the number-line.

 

 

  1. Solve for x:  x-2 -2x-1 = 8

 

  1. Solve 7 3x-1 = 15

 

  1. The number of grams of radioactive material present at time t is given by the formula y=y0ekt  where

t = time in years

y0 = the initial amount of material present at time t = 0

k = the rate of decay written as a negative decimal  (Eg:  -8.5% is written -.085)

y= the amount of material present at time t

 

 

 

  1. Solve x2 -8x +17 = 0 using the quadratic formula

 

 

  1. Big Tipper:  Write and solve a linear system in three variables:  On Monday, Aisha paid $1.70 for two cups of coffee and one doughnut, including tip.  On Tuesday she paid $1.65 for two doughnuts and a cup of coffee, including tip.  On Wednesday she paid $1.30 for one coffee and one doughnut, including the tip.  If she tips the same amount each time, what is the amount of each item?

 

 

 

 

  1. What transformations occur to the graph of y = |x| to obtain the graph of

y = -|x-2| +4?

 

 

 

 

  1. Composition of functions:  Let f(x) = 3x +5 and g(x) = x2 -2x

a)  Find g[f(x)]                              b)  Find f[f(x)]

 

 

 

 

  1. Graph g(x) = 2x + 1

 

 

 

  1. Solve log3(x) + log3 (x+6) = 3

 

 

 

 

 

  1. Expand log7(5y/x3z)

 

 

 

 

 

 

  1. Find the inverse of f(x) = 3x + 1

          8

 

 

 

 

 

  1. Prove that f(x) and f-1(x) above are inverses

 

 

 

 

 

  1. Write y = 2x2 -4x + 5 in the form y = a(x-h)2 + k.  The problem continues in #16.

 

a)  h= _________     b)  k= ____________   c)  axis of symmetry = _________________

16.  Identify the center and radius of the circle x2 + y2 -6x + 8y -9 = 15

 

 

 

Chapter 14 material:

 

  1. What is the difference between a sequence and a series?

 

 

2.  If a1 = 4, and d=6, a11 = ?   Write the formula that applies, then solve and simplify

 

 

 

 

  1. If b1 = -1, b7 = 11, d= __________

 

 

 

  1. Given the sequence 9, 3, 1, ….;  a9 = _______________.  Write the formula that applies, then solve.

 

 

 

 

 

4.  Write in Sigma notation, then find the sum:   S6 (  i – 2)

                                                                                         2

 

 

 

 

  1. Use the formula Sn = (n/2) (a1 + an) to find the sum of the first 46 positive integers.

 

 

 

6.  The number of otters born each year in a new aquarium forms a sequence whose general term is an = (n-1)(n+3).  Find the number of otters born each year during the first two years, and show the total sum of baby otters.